Following the rules as above, I would do 2^3 and then 3 x 7. But this is wrong, so my confusion is why the division comes before the first multiplication or is it simply a matter of how it's written?

This is exactly the ambiguity discussed in the last example at the bottom of this page. If the expression were "9/(3*7)", the meaning would be clear; as it is, it probably means "(9/3)*7". But "the" answer will vary with the technology (Excel, a TI-83, etc) or the source (a friend, two different instructors, etc).

Following the rules as above, I would do 2^3 and then 3 x 7. But this is wrong, so my confusion is why the division comes before the first multiplication or is it simply a matter of how it's written?

This is exactly the ambiguity discussed in the last example at the bottom of this page. If the expression were "9/(3*7)", the meaning would be clear; as it is, it probably means "(9/3)*7". But "the" answer will vary with the technology (Excel, a TI-83, etc) or the source (a friend, two different instructors, etc).